How to wrap paper around an object?
Cloth Sim

Add Circle 16 sides, Extrude, Scale, Grid Fill
Extrude, Scale outer loop, select vertices for each side and Scale on (X/Y) to zero to get square shape, add extra loops Ctrl+R+3



Add cloth simulation (physics)
Add ShrinkWrap modifier, select one vertex loop next to perfect circles and assign vertex group to these, and use this group for modifier
The illusion that brings cloth more to paper feeling is under Data Properties &gt; Normal &gt; Auto Smooth



To add detail to the lowpoly simulated mesh just add a Normal Map texture of smashed paper




Notes:

Select outer loop and with Proportional editing (O) rotate (R) a bit, twisted topology results in nicer sim

With a few extra loops close to existing folding is a bit closer to your reference.




To let border of paper stick closer to glass you can create another vertex group and use second Shrink-wrap modifier with a subtle Ofset value.